一种分裂形式CPR格式在欠解析流动中的稳定性研究

贾斐然; 朱华君; 严红; 燕振国; 石京昶

doi:10.7638/kqdlxxb-2022.0128

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一种分裂形式CPR格式在欠解析流动中的稳定性研究

研究论文 | 更新时间：2026-05-28

- 一种分裂形式CPR格式在欠解析流动中的稳定性研究
- On the stability of a split form CPR scheme in under-resolved flows
- 空气动力学学报 2023年41卷第11期页码：103-115
- 作者机构：
  
  1. 西北工业大学动力与能源学院,西安,710000
  2. 空气动力学国家重点实验室,绵阳,621000
- 作者简介：
  
  贾斐然(1998—)，男，四川人，硕士，研究方向：计算流体力学中的高精度算法及应用. E-mail：jiafeiran@mail.nwpu.edu.cn
  燕振国*，副研究员，研究方向：高精度算法及其软件开发和应用. E-mail：yanzhg@mail.ustc.edu.cn
- 基金信息：
  
  国家数值风洞工程（ NNW）;国家自然科学基金（12172375，11902344）;空气动力学国家重点实验室基金（SKLA2019010101）
- DOI：10.7638/kqdlxxb-2022.0128
  中图分类号： V211.3
- 纸质出版：2023
- 稿件说明：
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贾斐然, 朱华君, 严红, 等. 一种分裂形式CPR格式在欠解析流动中的稳定性研究[J]. 空气动力学学报, 2023, 41(11): 103−115.

JIA Feiran, ZHU Huajun, YAN Hong, et al. On the stability of a split form CPR scheme in under-resolved flows[J]. 2023, 41(11): 103-115.
贾斐然, 朱华君, 严红, 等. 一种分裂形式CPR格式在欠解析流动中的稳定性研究[J]. 空气动力学学报, 2023, 41(11): 103−115. DOI： 10.7638/kqdlxxb-2022.0128

JIA Feiran, ZHU Huajun, YAN Hong, et al. On the stability of a split form CPR scheme in under-resolved flows[J]. 2023, 41(11): 103-115. DOI： 10.7638/kqdlxxb-2022.0128.

摘要

基于重构的修正过程（correction procedure via reconstruction

CPR）方法是一种适用于非结构网格、紧致高效的高阶方法，但在离散非线性对流项时容易因为混淆误差的累积而出现数值不稳定。本文研究了基于LG （Legendre-Gauss）点分裂形式的CPR方法在欠解析流动中的稳定性，并将其与子单元限制技术结合，求解含激波的欠解析流动问题。结果表明：经过边界通量修正的LG点分裂形式CPR格式能够满足离散守恒律，且与子单元限制相结合后守恒律依然成立；在无激波的欠解析流动问题中，相比于散度形式CPR格式，分裂形式明显提高了计算的稳定性，而且比使用LGL（Legendre-Gauss-Lobatto）点的分裂形式CPR格式具有更小的数值误差；在含激波的欠解析流动求解中，相比基于LGL点的间断伽辽金谱元法子单元限制策略，基于LG点的分裂形式CPR格式子单元限制策略具有更高的分辨率和更小的振荡。

Abstract

The correction procedure via reconstruction (CPR) method is a compact and efficient high-order method suitable for unstructured grids. However

when discretizing the nonlinear convection term

it is easy to cause numerical instability due to the accumulation of aliasing errors. In the present work

we study the stability of the split form CPR method based on LG (Legendre-Gauss) points in under-resolved flows

and combine the method with the subcell limiting technique to solve under-resolved flows with shock waves. First

numerical tests are carried out to verify that the split form CPR method based on LG points with the boundary flux correction can satisfy the discrete conservation law

and such conservation is still preserved under subcell limiting. In the simulation of under-resolved flows without shock waves

compared to the divergence form CPR method

the split form significantly improves the stability of the calculation

and has smaller numerical errors than the split form CPR method using LGL (Legendre-Gauss-Lobatto) points. When solving under-resolved flows with shock waves

compared to the subcell limiting strategy of discontinuous Galerkin spectral element method based on LGL points

the subcell limiting strategy of split form CPR scheme based on LG points developed in this paper has higher resolution and less oscillation.

关键词

Keywords

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